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module

Synonym: 
left module, right module
Type of Math Object: 
Definition
Major Section: 
Reference
Groups audience: 

Mathematics Subject Classification

13-00 no label found16-00 no label found20-00 no label found44A20 no label found33E20 no label found30D15 no label found

Comments

The module definition does not require an identity element in the ring. Those satisfying 1 * m = m for all m in the module are called
unitary modules.
-- S.A. G.

Left (right) R modules M for rings R with identity 1 such that 1 * m = m (m * 1 = m) for all m in M are call unital modules.
-- S. A. G.

Left (right) R modules M for rings R with identity 1 such that 1 * m = m (m * 1 = m) for all m in M are called unital modules.
-- S. A. G.

Properties 1 through 4 are just the propreties of an abelian group. Wouldn't it be simpler to say that a module is an abelian group (M,+) with a binary operation . : R x M -> M that satisfies properties 5 through 7?

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